ENE 104 Electric Circuit Theory
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1 ENE 4 Electrc rcut Theory ecture 8: The R rcut (cont. : Dejwoot KHAWPARISUTH
2 ENE 4 Objectve : h9 The R rcut Page the charactertc dampng factor and reonant frequency for both ere and parallel R crcut overdamped, crtcally damped, and underdamped repone the complete repone op amp
3 ENE 4 The R rcut Summary: Page 3 R,
4 Example: Page 4 ENE 4 The R rcut
5 Example: Page 5 ENE 4 R From t dv t ( (. ( ( ( ( ( V t dv R R t ( A V ( 5 ( ( A V v v R. 4 V dv t The R rcut
6 ENE 4 The R rcut Example: v(t=m. Page 6 R 5F R H F 3.6 rad / t v( t e ( B co B n
7 ENE 4 Example: v(t=m. The R rcut Page 7 An underdamped /T d rad / t v( t e ( B co t B At t =, x B...(* ( And evaluatng the dervatve at t =, dx t n t ; B v( R B...(** d B
8 ENE 4 Example: v(t=m. The R rcut Page 8 v ( t t e ( B co t B n t ; B From dv ( t t dv ( t 4 B B B 6 v( t e t (co t 6n t v( t m..695 V.
9 ENE 4 The Source-Free Sere R /T: Page 9 The R rcut d R d t t ' R v ( t d dv R v d v t t v R ' ( t dv v
10 ENE 4 The R rcut The Sere R Repone: d R d The overdamped repone: Page t t ( t Ae Ae where, R R thu R and
11 ENE 4 The R rcut The Sere R Repone: d R d The overdamped repone: t t ( t Ae Ae Page The crtcally damped repone: t ( t e ( At A The underdamped repone: t ( t e ( B co B n, R, where d
12 ENE 4 The R rcut Summary: Page R,
13 Practce: 9.5 Page 3 ENE 4 The R rcut
14 ENE 4 Practce : The R rcut Page 4 R.5H.5H 4F 3.6 rad / ( ( A.
15 ENE 4 Practce : The R rcut Page 5 vr v 3.6 rad / ( A. from d v t ( t v ( d v ( v R (
16 ENE 4 Practce : (t=m. The R rcut Page 6 vr v An underdamped /T d rad / t ( t e ( B co B n ( A. 3.6 d rad / t t ( t e ( B co t B n t
17 ENE 4 Practce : (t=m. The R rcut Page 7 vr v An underdamped /T t x( t e ( B co B n x( B...(* dx B...(** d B t ( A. d d rad / t ; B ( ; B.5
18 ENE 4 Practce : (t=m. The R rcut Page 8 vr v d rad / B, B.5 An underdamped /T t x( t e ( B co B n ( t t e (co t.5n t ( m..4 A.
19 ENE 4 The omplete Repone: The R rcut Page 9 The complete repone = a force repone + a natural repone a force repone: v f ( t V f a natural repone: The complete repone: t t vn( t Ae Ae t t v( t Vf Ae Ae
20 ENE 4 Summary: The R rcut Page
21 Example: Page ENE 4 An R crcut that ued to llutrate everal procedure by whch the ntal condton may be obtaned. The dered repone nomnally taken to be v (t. The R rcut
22 ENE 4 Example: The R rcut Page t < R ( ( ( 5A. 5A. v v v R ( ( ( (5A. (3 5V. 5V.
23 Example: Page 3 ENE 4 t. ( ( (. 4 ( 5 (. 3 3 ( (. ( 4 (. 5 ( (. 5 ( ( V v v v A V v A V v v A R R R R R The R rcut
24 Example: Page 4 ENE 4 d t v ( from. / 4 3 ( A v d t. / 4 4 A d d therefore d d t R R R from. / 4 5 A d d therefore d d R t R R from The R rcut
25 Example: Page 5 ENE 4 dv t ( from. / 8 4 ( 7 V dv t. /... A dv t R from. / 9... A dv t from The R rcut
26 Practce: 9.6 Page 6 ENE 4 The R rcut et = u t u(t A. n Fgure. Fnd (a ( ; (b v ( + ; (c v R ( + ; (d,( ; (e.m.
27 Practce: 9.6 Page 7 ENE 4 The R rcut et = u t u(t A. n Fgure. Fnd (a ( ; (b v ( + ; (c v R ( + ; (d,( ; (e.m.
28 Practce: 9.6 Page 8 ENE 4 The R rcut et = u t u(t A. n Fgure. Fnd (a ( ; (b v ( + ; (c v R ( + ; (d,( ; (e.m.
29 Practce: 9.7 Page 9 ENE 4 The R rcut
30 Practce : Page 3 ENE 4 The R rcut
31 Practce : Page 3 ENE 4 The R rcut
32 Practce : Page 3 ENE 4 The R rcut
33 Practce: 9.8 Page 33 ENE 4 The R rcut Gve new value for R f and the two ntal voltage n the crcut on the left f the output repreent the voltage v(t n the crcut on the rght.
34 Practce: 9.8 Page 34 ENE 4 The R rcut
35 Practce: 9.8 Page 35 ENE 4 The R rcut
36 Example: Ex 4 Page 3 Page 36 ENE 4 The R rcut Fnd - (t - At what ntant of tme after t = ( t?
37 Example: Ex 4 Page 3 Page 37 ENE 4 The R rcut Sere R: R.H 5.H 4F 5 rad /
38 Example: Ex 4 Page 3 Page 38 ENE 4 The R rcut Sere R: rtcally damped ( t x( t X e B t B x( X B f f ' ' ' dx t B ' B '
39 Example: Ex 4 Page 3 Page 39 ENE 4 The R rcut Sere R: rtcally damped ( t ( t I e B t B ( I B f f ' ' ' d t B ' B '
40 Example: Ex 4 Page 3 Page 4 ENE 4 The R rcut Sere R: rtcally damped ( t ( t I e B t B f ' ' ( 3 d ( I B t f B ' ' B ' I f 3( 3 v ( 3
41 Example: Ex 4 Page 3 Page 4 ENE 4 The R rcut Sere R: rtcally damped ( d t ( t I e B t B ( I B t f f B ' ' B ' ' ' d t v( v ( vr ( 3 3
42 Example: Ex 4 Page 3 Page 4 ENE 4 The R rcut Sere R: rtcally damped ( d t ( t I e B t B ( I B t f f B ' ' B ' ' ' B ' B ' 6 3
43 Example: Ex 4 Page 3 Page 43 ENE 4 The R rcut Sere R: rtcally damped ( ( t 3 e 5t 3t 6, t ( t 3u( t 5t 3 e 3t 6 u( t
44 Example: Ex 4 Page 3 Page 44 ENE 4 The R rcut Fnd - At what ntant of tme after t = ( t? From ( t 3 e 5t 3t 6, t ( t 3 e 5t t 3.357m. 3t 6
45 Example: Ex 43 Page 3 Page 45 ENE 4 The R rcut Wth =[+u(t] A. Fnd (t
46 Example: Ex 43 Page 3 Page 46 ENE 4 The R rcut Parallel R: R mh.5f 6
47 Example: Ex 43 Page 3 Page 47 ENE 4 The R rcut Parallel R: Underdamped ( d ( I, f v (
48 Page 48 Example: Fnal /46 (Ex49 p3 ENE 4 The R rcut ในวงจร ตามร ป แหล งจ ายกระแส เปล ยนค าจาก 5 A. เป น A. ท นท ท นใด ท เวลา t = จงหา v (, v (, v (, and v (3.4.
49 Page 49 Example: Fnal /46 (Ex49 p3 ENE 4 The R rcut v v ( ( 5A. 3 ( 3 v ( ( ( 3 v 5 ( v ( A. 44 v (
50 Example: Fnal /47 Page 5 ENE 4 The R rcut 5 ohm 5 V k ohm t = + F v o -.6 H Fnd ( t vo ( t d( dvo ( ( t v o ( t
51 Example: Fnal /47 Page 5 ENE 4 The R rcut v ( t ( ( t ( 5 5 o v d ( dvo ( v ( ( ohm.5 5 V k ohm t = + F v o -.6 H
52 Example: Fnal /47 Page 5 ENE 4 The R rcut dvo ( (... From v ( 5 5 v ( ( ( 5 ohm 5 V k ohm t = + F v o -.6 H
53 ENE 4 Ex: The R rcut Page 53 สำหร บวงจร R แบบขนำนท ม voltage repone v( t 4t 4t Dte De, t ค ำ ntal current ในต ว nductor ม ค ำ 5 ma, และ ค ำ ntal voltage ในต วเก บประจ ม ค ำ 5 V. โดยท ค ำ nductance ของต ว nductor ม ขนำด 5 H. ให หำ a ค ำของ R,, D, D b (t สำหร บ t > +
54 Ex: Page 54 ENE 4 The R rcut
55 Ex: Page 55 ENE 4 The R rcut
56 ENE 4 Ex: The R rcut Page 56 5 ohm 5 V kohm F t = +.6 H v o - ให หำ a v o ( t, t b ( t, t
57 ENE 4 Ex: The R rcut Page 57 5 ohm 5 V kohm F t = + v o.6 H -
58 ENE 4 Ex: The R rcut Page 58 5 ohm 5 V kohm F t = + v o.6 H -
59 Hw: Page 59 ENE 4 The R rcut
60 ENE 4 Reference: rcut Analy and Electrcal Engneerng Page 6 W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbn, Engneerng rcut Analy, Sxth Edton. opyrght McGraw-Hll. All rght reerved.
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